Solution of a linear inequality
Identify solutions to linear inequalities in Grade 9 algebra: any ordered pair (x,y) making the inequality true is a solution, represented by the shaded region on one side of the boundary line.
Key Concepts
Property A solution of a linear inequality is any ordered pair that makes the inequality true. Explanation Think of it like a true/false test for coordinates! You plug the $(x, y)$ values from an ordered pair into the inequality. If the resulting statement is true, you've found a solution and that point is in the club! If it's false, that point is not invited to the party. Examples Is $(2, 5)$ a solution of $y 2x + 1$? $5 2(2) + 1$ becomes $5 5$, which is false. Not a solution. Is $(1, 8)$ a solution of $y \ge 3x + 5$? $8 \ge 3(1) + 5$ becomes $8 \ge 8$, which is true. It is a solution. Is $( 3, 4)$ a solution of $y < 2x 1$? $4 < 2( 3) 1$ becomes $4 < 5$, which is true. It is a solution.
Common Questions
What is a solution to a linear inequality in two variables?
A solution is any ordered pair (x, y) that makes the inequality true when substituted. For y < 2x + 3, the pair (0, 0) is a solution because 0 < 3 is true. The entire shaded region on the graph represents all solutions.
How do you determine which ordered pairs are solutions to a linear inequality?
Substitute each x and y value into the inequality. If the resulting statement is true, the ordered pair is a solution. If false, it is not. For y ≥ x - 2, test (3, 1): 1 ≥ 3 - 2 = 1. True, so (3,1) is a solution.
How does the graph of a linear inequality show all solutions?
Graph the boundary line (solid for ≤/≥, dashed for </>). Test a point to find which side satisfies the inequality. Shade that entire half-plane — every point in the shaded region is a solution to the inequality.